Numerical solution of European call option with dividends and variable volatility |
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| Authors: | U.S. Rana Asad Ahmad |
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| Affiliation: | a Department of Mathematics, D.A.V. (P.G.) College, Dehradun, Uttrakhand 248001, India
b Department of Mathematics, TechWords W.G.V.S. Group of Institutions, Manglour Roorkee, Haridwar, Uttrakhand 248001, India |
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| Abstract: | In this paper, the effect of strike price, interest rate, dividends and maturities on European call option with dividends is discussed. The volatility for the data of ONGC Ltd. listed in National Stock Exchange, India, during 03-01-2000 to 30-03-2009 is forecasted by GJR-GARCH method. The option price and Greeks are determined by solving modified Black-Scholes partial differential equation by adjusting forecasted volatility at each grid point of finite difference method. It is observed that call option premium decreases as strike price and dividend increases but it increases as rate of interest and time of maturities increases. Hence call option is more profitable for a long maturity, high interest rate and low dividend. |
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| Keywords: | Stochastic volatility Finite difference method European option Continuous dividends |
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